$ \lim_{x\to 4}\dfrac{2x+1}{-3x+3}=$
Answer: $\dfrac{2x+1}{-3x+3}$ defines a rational function. Rational functions are continuous across their entire domain, and their domain is all real $x$ -values that don't make the denominator equal to zero. In other words, for any rational function $r$ and any input $c$ in the domain of $r$, we know that this equality holds: $\lim_{x\to c}r(x)=r(c)$ The input $x=4$ is within the domain of $\dfrac{2x+1}{-3x+3}$. Therefore, in order to find $ \lim_{x\to 4}\dfrac{2x+1}{-3x+3}$, we can simply evaluate $\dfrac{2x+1}{-3x+3}$ at $x=4$. $\begin{aligned} &\phantom{=}\dfrac{2x+1}{-3x+3} \\\\ &=\dfrac{2(4)+1}{-3(4)+3} \gray{\text{Substitute }x=4} \\\\ &=\dfrac{9}{-9} \\\\ &=-1 \end{aligned}$ In conclusion, $ \lim_{x\to 4}\dfrac{2x+1}{-3x+3}=-1$.